Doppler ultrasound is used to measure the speed of blood flow. If the speed of t

Question

Doppler ultrasound is used to measure the speed of blood flow. If the speed of the red blood cells is v, the speed of sound in blood is u, the ultrasound source emits waves of frequency f, and we assume that the blood cells are moving directly toward the ultrasound source, then the frequency fr of reflected waves detected by the apparatus is given by the formula below. fr = f 1 + v/u 1 ? v/u The reflected sound interferes with the emitted sound, producing beats. If the speed of red blood cells is 0.15 m/s, the ultrasound frequency used is 4.9 MHz, and the speed of sound in blood is 1570 m/s, what is the beat frequency?

Explanation / Answer

You know the frequency of the ultrasound source. You can calculate the frequency of the doppler-shifted return signal as Ft=f*(1+v/c)/(1-v/c). You can do this because you know that F=5.7MHz v=0.11m/s c = 1570m/s Just plug in the numbers to calculate Ft. The beat frequency is simply the difference between F and Ft So if F = 5.7 MHz, and you calculate Ft to be 5.8MHz, the beat frequency would be 5.8 - 5.7 = 0.1 MHz

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